PART 1 Answer

YES – the extrapolated efficiency makes sense.

The active area of a typical GM pancake is 15 cm², which gives it a radius of 2.19 cm.

If we assume that the area of the source << than the detector area, and that the detector window is 1 cm from the source, we can calculate the geometry factor as follows.

• Angle of cone:

• Solid angle:

            2π(1-cos (66°)) = 3.73 steradians

• Geometry factor is 3.73/4π= 0.3

Gamma efficiency:

A GM pancake is gas filled and thus expected to have a very low efficiency (≈ 0.5%) for a high energy gamma. Applying this factor, and knowing that the high energy gamma is emitted about 50% of the time, the gamma efficiency is calculated as follows:

            0.5% (efficiency) x 0.3 (geometry factor) x 0.5 ỿ/decay = 0.075%

Beta efficiency:

A GM pancake is expected to have essentially 100% efficiency for any beta that gets through the window. From the presentation slide (below) showing the beta spectra and cutoff, we can estimate that at 330 keV, roughly 50% of the betas, will get through window.

            100% (efficiency) x 0.014 β+/decay x 0.5 (window losses) x 0.3 (geometry factor) = 0.21%

The total efficiency is therefore 0.21% + 0.075% = 0.29%. This is on the same order of magnitude and compares well with the extrapolated efficiency of 0.33%.

PART 2 Answer

NO – the MDA is not low enough to satisfy CNSC contamination detection requirements.

The MDA, in units of Bq/cm², is calculated from the following equation:

In this example:

• NB = 30 CPM
• T = 600
• E = 0.0033
• A = 100
• F = 0.1 (default value given in the presentation)

The calculated MDA is 4.2 Bq/cm². This exceeds the contamination limit, which for Zn-65 (a class C radionuclide) is 3 Bq/cm² for controlled areas.

PART 3 Answer

NO – the MDA is not low enough to be used for direct measurement.

For direct measurements, we can use the same formula as above with two changes:

• There is no value for F. Since we are not taking a swipe, there is no swipe efficiency to be considered. (Alternatively, you can consider that there is in fact full efficiency in this case, for which the value of F would be 1. The end result is the same).
• The area for the calculation, A, is now only 15 cm²; for a direct check, we use the area of the detector.

Running through the calculation with these values, we get an MDA of 2.8 Bq/cm², which is below the limit of 3 Bq/cm².

BUT we’re not done — don’t forget to include the uncertainty!

The 2σ uncertainty is calculated using the following formula:

Again, for this example

• T = 600
• E = 0.0033
• A = 15

But what is N?

• At 2.8 Bq/cm², the total contamination over a 15 cm² area is 42 Bq.
• We already know that the efficiency is 0.033 at 1 cm, so the measured count rate, N, should be:
  Bq x 0.0033 = 0.14 cps or 8.4 CPM above background

The 2σ uncertainty calculated from the formula above is then 1.3 Bq/cm².

Therefore, the MDA plus the 2ơ uncertainty (the upper bound) is 4.1 Bq/cm², which is greater than the contamination limit of 3 Bq/cm².

(Note: Even if this was below the limit, a 10 minute dwell time for a direct measurement is not practical)